1. Objectives Solve quadratic equations by completing the square.
Write quadratic equations in vertex form.

2. Vocabulary
completing the square

3. Read as “plus or minus square root of a.”
Reading Math

4. Example 1: Solving Equations by Using the Square Root Property
Solve the equation.
x2 = 121

5. Example 1: Solving Equations by Using the Square Root Property
Solve the equation.
x2 = 121 Is this the same as “What is the
√(121)?”

6. Example 2: Solving Equations by Using the Square Root Property
Solve the equation.
x2 = 1296

7. Example 3: Solving Equations by Using the Square Root Property
Solve the equation.
4x = 59

8. Example 4
Solve the equation.
4x2 – 20 = 5

9. If a quadratic expression of the form x2 + bx cannot model a square, you can add a term to form a perfect square trinomial. This is called completing the square.

10. Example 5: Completing the Square
Complete the square for the expression. Write the resulting expression as a binomial squared.
x2 – 14x +

11. Example 6: Completing the Square
Complete the square for the expression. Write the resulting expression as a binomial squared.
x2 + 9x +

12. Example 7
Complete the square for the expression. Write the resulting expression as a binomial squared.
x2 + 4x +

13. Example 8
Complete the square for the expression. Write the resulting expression as a binomial squared.
x2 – 4x +

14. Example 9
Complete the square for the expression. Write the resulting expression as a binomial squared.
x2 + 3x +

15. You can complete the square to solve quadratic equations.

16. Example 11: Solving Equations
Solve the equation.
x2 + 12x + 6 = 0

17. Example 12
Solve the equation.
x2 + 8x - 33 = 0

18. Example 13: Solving a Quadratic Equation by Completing the Square
Solve the equation by completing the square.
x2 = 12x – 20

19. Example 14: Solving a Quadratic Equation by Completing the Square
Solve the equation by completing the square.
18x + 3x2 = 45

20. Example 15
Solve the equation by completing the square.
x2 – 2 = 9x

21. Example 16
Solve the equation by completing the square.
3x2 – 24x = 27